Distribution shapes govern the discovery of predictive models for gene regulation

Munsky, Brian; Li, Guoliang; Fox, Zachary; Shepherd, Douglas P.; Neuert, Gregor

doi:10.1073/pnas.1804060115

Cited by 100 publications

(190 citation statements)

References 40 publications

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“…In this article, we adopted a Markov chain Monte Carlo algorithm with Metropolis-Hastings sampling (i.e., MCMC-MH) to compute the posterior distributions of the model parameters [15,45]. However, there is room to further improve the speed of Bayesian inference.…”

Section: Discussionmentioning

confidence: 99%

Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Lin

2018

Preprint

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Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to statistical inference is the most complete method for model selection and uncertainty quantification of kinetic parameters from single-cell data. This approach is impractical because current numerical algorithms are too slow to handle typical models of gene expression. To solve this problem, we first show that time-dependent mRNA distributions of discrete-state models of gene expression are dynamic Poisson mixtures, whose mixing kernels are characterized by a piece-wise deterministic Markov process. We combined this analytical result with a kinetic Monte Carlo algorithm to create a hybrid numerical method that accelerates the calculation of time-dependent mRNA distributions by 1000-fold compared to current methods. We then integrated the hybrid algorithm into an existing Monte Carlo sampler to estimate the Bayesian posterior distribution of many different, competing models in a reasonable amount of time. We validated our method of accelerated Bayesian inference on several synthetic data sets. Our results show that kinetic parameters can be reasonably constrained for modestly sampled data sets, if the model is known a priori. If the model is unknown,the Bayesian evidence can be used to rigorously quantify the likelihood of a model relative to other models from the data. We demonstrate that Bayesian evidence selects the true model and outperforms approximate metrics, e.g., Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC), often used for model selection.

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Section: Discussionmentioning

confidence: 99%

Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Lin

2018

Preprint

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“…For example, application of noisy dynamical systems theory has shed light on cell-state transitions (Mojtahedi et al, 2016;Jin et al, 2018;Lin et al, 2018). Stochastic simulations of gene network dynamics have been used to develop and/or benchmark tools for network reconstruction (Schaffter et al, 2011;Dibaeinia and Sinha, 2019;Bonnaffoux et al, 2019) Stochastic model-aided analysis of single-cell measurements has been demonstrated to yield insights on gene regulatory mechanisms (Munsky et al, 2018). However, few existing analysis methods utilize discretemolecule, stochastic models, which fully account for intrinsic gene expression noise and its impact on cell-state, to aid in the interpretation of noisy distributions recovered from single cell RNA sequencing data.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Single-Cell Gene Pair Coexpression Landscapes by Stochastic Kinetic Modeling Reveals Gene-Pair Interactions in Development

2020

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Single-cell transcriptomics is advancing discovery of the molecular determinants of cell identity, while spurring development of novel data analysis methods. Stochastic mathematical models of gene regulatory networks help unravel the dynamic, molecular mechanisms underlying cell-to-cell heterogeneity, and can thus aid interpretation of heterogeneous cell-states revealed by single-cell measurements. However, integrating stochastic gene network models with single cell data is challenging. Here, we present a method for analyzing single-cell gene-pair coexpression patterns, based on biophysical models of stochastic gene expression and interaction dynamics. We first developed a high-computational-throughput approach to stochastic modeling of gene-pair coexpression landscapes, based on numerical solution of gene network Master Equations. We then comprehensively catalogued coexpression patterns arising from tens of thousands of gene-gene interaction models with different biochemical kinetic parameters and regulatory interactions. From the computed landscapes, we obtain a lowdimensional "shape-space" describing distinct types of coexpression patterns. We applied the theoretical results to analysis of published single cell RNA sequencing data and uncovered complex dynamics of coexpression among gene pairs during embryonic development. Our approach provides a generalizable framework for inferring evolution of gene-gene interactions during critical cell-state transitions.

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“…Studies at single-cell resolution are crucial to this, enabling the full distribution of expression levels to be obtained over a population of cells. Such data not only provides qualitative insight into the variability between cells, but can also enable the inference of the underlying dynamical processes ( Munsky et al, 2018 ), through the combination of biological insight and quantitative models. This is the approach we take here to investigate the sources of noise that lead to heterogeneity of nifHDK gene expression at the transcriptional level.…”

Section: Introductionmentioning

confidence: 99%

Molecular origins of transcriptional heterogeneity in diazotrophicK. oxytoca

Bashir

Brackston

et al. 2020

Preprint

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Phenotypic heterogeneity in clonal bacterial batch cultures is an important adaptive 10 strategy to changing environments, including in diazotrophs with the unique capacity to convert 11 di-nitrogen into bio-available ammonium. In diazotrophic Klebsiella oxytoca we simultaneously 12 measured mRNA levels of key regulatory (glnK-amtB, nifLA) and structural (nifHDK) operons required 13 for establishing nitrogen fixation, using dual molecule, single cell RNA-FISH. Through stochastic 14 transcription models and mutual information analysis we revealed likely molecular origins for 15 heterogeneity in nitrogenase expression. In wildtype and regulatory variant strains we inferred 16 contributions from intrinsic and extrinsic noise, finding that nifHDK transcription is inherently 17 bursty, but that noise propagation through signalling is also significant. The regulatory gene glnK 18 had the highest discernible effect on nifHDK variance, while noise from factors outside of the 19 regulatory pathway were negligible. Results provide evidence that heterogeneity is a fundamental 20 property of this regulatory system, indicating potential constraints for engineering homogeneous 21 nitrogenase expression. 22 30 Phenotypic heterogeneity may be particularly relevant in costly stress response systems, of 31 which the response to nitrogen starvation is a key example (Schreiber et al., 2016). In organisms 32 such as Klebsiella oxytoca, nitrogen starvation triggers a transition to diazotrophic behaviour in 33 which bacterial cells use atmospheric di-nitrogen as their nitrogen source for growth (Dixon and 34 Kahn, 2004). While this transition, and the associated transcriptional programme, is essential 35 for continued growth under conditions deplete of fixed nitrogen, it is also very costly since the 36 resultant ATP consuming nitrogenase enzyme may ultimately constitute up to 20 % of the proteome 37 (Dixon and Kahn, 2004). As such, if fixed nitrogen sources soon become available again, it is likely 38 advantageous to have not fully undergone the diazotrophic transition. Activation of the nitrogen 39 stress response is potentially somewhat of a gamble in which the payoff depends strongly on future 40 1 of 15conditions. Such a scenario may therefore indicate a requirement for bet-hedging strategies in 41 which heterogeneity proves advantageous at the population level (van Boxtel et al., 2017). 42 Regardless of whether there are advantages to heterogeneity, it is also important to establish 43 the underlying mechanistic causes, especially if there is an aim to ultimately modify cell behaviour. 44 Studies at single-cell resolution are crucial to this, enabling the full distribution of expression levels 45 to be obtained over a population of cells. Such data not only provides qualitative insight into the 46 variability between cells, but can also enable the inference of the underlying dynamical processes 47 and predicts the probability distribution of mRNA copy numbers (Ko, 1991; Peccoud and Ycart, 1995; 87 ., 2006;...

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Distribution shapes govern the discovery of predictive models for gene regulation

Cited by 100 publications

References 40 publications

Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Accelerated Bayesian inference of gene expression models from snapshots of single-cell transcripts

Analysis of Single-Cell Gene Pair Coexpression Landscapes by Stochastic Kinetic Modeling Reveals Gene-Pair Interactions in Development

Molecular origins of transcriptional heterogeneity in diazotrophicK. oxytoca

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